Question

A particle is projected with a velocity u at an angle theta with the horizontal . find the radius of curvature of the parabola traced out by the particle at the point where velocity makes an angle of theta / 2 with horizontal

Answer 1

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Answer:
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Given that the initial velocity of the particle is U. The object is projected at an angle θ. Then the horizontal and vertical components of the initial velocity are,

Ux=U cos θ
&
Uy=U sin θ

Let after t time of projection, the particle is making an angle θ2/. Therefore,

V cos (θ2/)=U cos θ⇒V=U cos θcos (θ2/)

∴V sin (θ2/)=(U cos θcos (θ2/))×sin (θ2/)